Automorphic loops and metabelian groups

Given a uniquely 2-divisible group $G$, we study commutative loop $(G,\circ)$ which arises as result of construction in ``Engelsche elemente noetherscher gruppen'' (1957) by R. Baer. We investigate some general properties and applications ``$\circ$'' determine necessary sufficient condition on $G$ order for $(G, \circ)$ to be Moufang. In ``A class loops categorically isomorphic Bruck odd order'' (2014) M. Greer, it is conjectured that metabelian if only an automorphic loop. answer portion this conjecture the affirmative: particular, show split order, then automorphic.